Ishaan thought it would be nice to include $\frac{3}{28}$ of a pound of chocolate in each of the holiday gift bags he made for his friends and family. How many holiday gift bags could Ishaan make with $\frac{3}{4}$ of a pound of chocolate?
Solution: To find out how many gift bags Ishaan could create, divide the total chocolate ( $\frac{3}{4}$ of a pound) by the amount he wanted to include in each gift bag ( $\frac{3}{28}$ of a pound). $ \dfrac{{\dfrac{3}{4} \text{ pound of chocolate}}} {{\dfrac{3}{28} \text{ pound per bag}}} = {\text{ number of bags}} $ Dividing by a fraction is the same as multiplying by the reciprocal. The reciprocal of ${\dfrac{3}{28} \text{ pound per bag}}$ is ${\dfrac{28}{3} \text{ bags per pound}}$ $ {\dfrac{3}{4}\text{ pound}} \times {\dfrac{28}{3} \text{ bags per pound}} = {\text{ number of bags}} $ $ \dfrac{{3} \cdot {28}} {{4} \cdot {3}} = {\text{ number of bags}} $ Reduce terms with common factors by dividing the $3$ in the numerator and the $3$ in the denominator by $3$ $ \dfrac{{\cancel{3}^{1}} \cdot {28}} {{4} \cdot {\cancel{3}^{1}}} = {\text{ number of bags}} $ Reduce terms with common factors by dividing the $28$ in the numerator and the $4$ in the denominator by $4$ $ \dfrac{{1} \cdot {\cancel{28}^{7}}} {{\cancel{4}^{1}} \cdot {1}} = {\text{ number of bags}} $ Simplify: $ \dfrac{{1} \cdot {7}} {{1} \cdot {1}} = {7} $ Ishaan could create 7 gift bags.